Question

在一场二十道题的测试中，每答对一题得 $5$ 分，未作答一题得 $1$ 分，答错一题得 $0$ 分。下列哪个分数不可能出现？

On a twenty-question test, each correct answer is worth $5$ points, each unanswered question is worth $1$ point and each incorrect answer is worth $0$ points. Which of the following scores is NOT possible?

$90$

$91$

$92$

$95$

$97$

答案：E

知识点：分类讨论

难度评级：1550

解答：

答对 $20$ 题时，分数是 $100$ 。

答对 $19$ 题时，根据剩下一题是答错还是未作答，分数是 $95$ 或 $96$ 。

答对 $18$ 题时，剩下两题可以贡献 $0$ 、 $1$ 或 $2$ 分，所以可得 $90$ 、 $91$ 或 $92$ 。

因此列出的分数 $90,91,92,95$ 都可能，而 $97$ 不可能。

所以正确答案是 E。

With $20$ correct answers, the score is $100$ .

With $19$ correct answers, the score is either $95$ or $96$ , depending on whether the remaining question is incorrect or unanswered.

With $18$ correct answers, the remaining two questions can contribute $0$ , $1$ , or $2$ points, giving $90$ , $91$ , or $92$ .

Thus the listed scores $90,91,92,95$ are possible, while $97$ is not.

Thus, E is the correct answer.

2001 AMC 8 第 22 题

答案：E

难度评级：1550

解答：

其他年份的第 22 题